A stationery stall had pens and pencils in the ratio 4 : 5 at first. The stall sold 12 pens and received 24 more pencils. After this, the ratio of the number of pens to the number of pencils became 1 : 2. How many pencils were there at the stall after this?
- 80
- 104
- 128
- 52
Need a hint?
Write the pencils after the change in terms of k, then use the new ratio 1 : 2 to form an equation for k. Do not forget to add the 24 pencils received.
Worked answer
- At first, pens : pencils = 4 : 5, so let 1 unit = k: pens = 4k, pencils = 5k.
- After the sale, pens = 4k − 12 and pencils = 5k + 24.
- After this, pencils = 2 × pens, so 5k + 24 = 2 × (4k − 12).
- 5k + 24 = 8k − 24, so 3k = 48 and k = 16.
- Pencils after the change = 5 × 16 + 24 = 104.
Answer: 104 pencils
The mistake this question tests
Habit
Calculation slip
Pupils often pick the pencil count at first (80) and forget that 24 pencils were received, or they find the first total and stop there.
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